In our research, we propose two improve methods for detection of dominant points for a digitized curve. Instead of setting a fixed length of support region, it will compute the suitable length of support region for each point to find the best approximated curvature. First, the symmetric region of support for each point on curve is determined using diagonal value. The points with local maximum averaging diagonal value can be located as the dominant points on the curve. Second, the improve method uses an optimal criterion for determining the asymmetric region of support of each boundary point, and a new mechanism for selecting the dominant points.